Contemporary Mathematics 1st Edition OpenStax - Solutions

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What is the value of the golden ratio to the nearest thousandth?
What are the first 10 terms of the Fibonacci sequence?
What is a golden rectangle?
What is the relationship between \(1 \mathrm{~kW}\) and watts?
An average bath uses about \(35 \mathrm{gal}\) of water. A water-saving showerhead uses approximately 2 gal of water per minute. If a person typically takes one bath a week, how much water is saved by replacing the baths with showers lasting 5 minutes over the course of a month?
How long does it take for a \(30 \mathrm{~W}\) Google Nest audio to use \(1 \mathrm{~kW}\) of power?
How long would it take for a \(60 \mathrm{~W}\) bulb to consume \(1 \mathrm{~kW}\) of power? Round your answer to the nearest hour.
What two pieces of information are needed to calculate the volume of a prescription drug to be dispensed?
Research on coronavirus vaccines began in 2020.a. Trueb. False
What is mathematical modeling, and how is it used in the world of medicine with pandemics?
What is the difference between frequency and pitch of a note?
Are higher frequencies associated with higher or lower pitch notes?
What frequency range can humans hear?
As a sound appears louder, does the decibel value increase or decrease?
What is the lowest decibel value that most people can hear?
What is the typical audible frequency range that adults can hear?
How does the frequency of a note change when increased by one octave?
How is data analytics used in sports today?
What is the most popular sport in today's world?
What is the formula to compute the number of games played in a single round-robin tournament with \(n\) teams assuming single round?
What is the formula to compute the number of games played in a single-elimination tournament?
Gas lawn mower: \(70 \mathrm{~dB}, 100 \mathrm{~dB}, 120 \mathrm{~dB}\)Select the most representative decibel level for each sound.
Radio playing loud enough to sing along to at home: \(20 \mathrm{~dB}, 50 \mathrm{~dB}, 70 \mathrm{~dB}\)Select the most representative decibel level for each sound.
Office noise on a floor of people working at desks: \(40 \mathrm{~dB}, 60, \mathrm{~dB}, 80 \mathrm{~dB}\)Select the most representative decibel level for each sound.
Conversation in a quiet room: \(60 \mathrm{~dB}, 80 \mathrm{~dB}, 100 \mathrm{~dB}\)Select the most representative decibel level for each sound.
Fast-moving train passing by when sitting in a car about \(20 \mathrm{ft}\) from the tracks with windows down: \(40 \mathrm{~dB}, 60 \mathrm{~dB}\), \(80 \mathrm{~dB}\)Select the most representative decibel level for each sound.
What is one half-step above \(G^{\#}\) ?State the requested note.
What is one whole step down from \(G^{b}\) ?State the requested note.
What is three half-steps above \(D\) ?State the requested note.
What is two whole steps down from \(A^{\#}\) ?State the requested note.
What is two half-steps down from \(E\) ?State the requested note.
What is an octave above \(B_{4}\) ?State the requested note.
What is two octaves below \(F_{5}\) ?State the requested note.
What is three octaves above \(\mathrm{G}_{2}\) ?State the requested note.
What is an octave below \(G_{2}\) ?State the requested note.
Given that the frequency of \(A_{4}=440 \mathrm{~Hz}\), what is the frequency of \(A_{1}\) ?
Given that the approximate frequency of \(\mathrm{F}_{4}=349 \mathrm{~Hz}\), what is the approximate frequency of \(\mathrm{F}_{5}\), rounded to the nearest whole number?
Given that the approximate frequency of \(A_{4}{ }^{\#}=233 \mathrm{~Hz}\), what is the approximate frequency of \(A_{6}{ }^{\#}\), rounded to the nearest whole number?
Given that the approximate frequency of \(\mathrm{D}_{4}=294 \mathrm{~Hz}\), what is the approximate frequency of \(D_{2}\), rounded to the nearest whole number?
Given that the approximate frequency of \(\mathrm{G}_{4}{ }^{\#}=349 \mathrm{~Hz}\), what is the approximate frequency of \(\mathrm{G}_{3}{ }^{\#}\), rounded to the nearest whole number?
Given that the frequency of \(A_{3}=220 \mathrm{~Hz}\), what is the frequency of \(A_{5}\) ?
Briefly describe data analytics.
Name a sport's career title that relies on analysis of data.
How many games would be played with 4 teams using a round-robin tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 8 teams using a round-robin tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 10 teams using a round-robin tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 25 teams using a round-robin tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 12 teams using a round-robin tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 4 teams using a single-elimination tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 9 teams using a single-elimination tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 15 teams using a single-elimination tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 50 teams using a single-elimination tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
How many games would be played with 24 teams using a single-elimination tournament?Compute how many games would be played in the style of tournament and number of teams given in each question. Assume all tournaments are single round-robin or single-elimination.
If a person's height is \(5 \mathrm{ft} 6 \mathrm{in}\), what is the approximate length from their belly button to the floor rounded to the nearest inch, assuming the ratio is golden?
Suppose you were creating a rose out of icing, assuming a Fibonacci sequence in the petals, how many petals would be in the row following a row containing 13 petals?
The 24th Fibonacci number is 46,368 and the 25 th is 75,025 . Show that the ratio of the 25 th and 24th Fibonacci numbers is approximately \(\phi\). Round your answer to the nearest thousandth.
A frame has dimensions of 8 in by \(6 \mathrm{in}\). Calculate the ratio of the sides rounded to the nearest thousandth and determine if the size approximates a golden rectangle.
Brushing your teeth with the water running continually uses about 4 gal of water. Turning the faucet off when you are not rinsing uses less than one-fourth of a gallon of water. Considering the recommendation to brush your teeth twice a day, how much water would be saved in a week if the faucet was
Using the data in Example 13.5, how much water would be saved in a month if one-fifth of a town's population of 15,000 turned the faucet off when brushing their teeth except when rinsing?
Using the data in Example 13.5, how much water would be saved in a year if one-fourth of the population of the state of Minnesota, which is approximately 5.6 million people, turned the faucet off when brushing their teeth except when rinsing for a year ( 52 weeks)?
A 48 in plasma television uses about 200 W. How many kilowatt-hours are needed to run the television in a month if the television is one for an average of 2.5 hours a day?
A medium-sized Energy Star-rated refrigerator uses about \(575 \mathrm{~W}\) and runs for about 8 hours per day. What is the monthly ( 30 days) cost of running the refrigerator if the electric rate is 12 cents per kilowatt-hour?
An electric oven is labeled as 4,000 W. How much would it cost to bake a cake for 30 minutes if the electric rate is 14 cents per kilowatt-hour?
If a home uses approximately \(30 \mathrm{~kW}\) of electricity per day, what size solar system would be needed to fuel \(80 \%\) of a home's needs for a month (30 days)?
How much sodium bicarbonate is there in a \(250 \mathrm{~mL}\) solution of \(1.58 \% \mathrm{w} / \mathrm{v}\) sodium bicarbonate?
A doctor prescribes \(25.5 \mathrm{mg}\) of a drug to take orally per day and pills are available in \(8.5 \mathrm{mg}\). How many pills will be needed each day?
A patient is prescribed \(2 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered intramuscularly, divided into 3 doses per day. If the patient weighs \(45 \mathrm{~kg}\), how many milligrams of the drug should be given per dose?
A patient is prescribed \(2 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered intramuscularly, divided into 3 doses per day. If the drug is available in \(20 \mathrm{mg} / \mathrm{mL}\) and the patient weighs \(60 \mathrm{~kg}\), how many milliliters of the drug should be given per dose?
For the following exercises, use the sample contact tracing graph to identify paths (Figure 13.12).1. How many people have a path of length 2 from Jeffrey?2. Find 2 paths between Kayla and Rohan.3. Find the shortest path between Yara and Kalani. State the length and people in the path. Yara Aishal
Select the most representative decibel value for each of the following sounds:1. car wash: \(25 \mathrm{~dB}, 55 \mathrm{~dB}, 85 \mathrm{~dB}\)2. vacuum cleaner: \(15 \mathrm{~dB}, 70 \mathrm{~dB}, 90 \mathrm{~dB}\)3. ship's engine room: \(30 \mathrm{~dB}, 65 \mathrm{~dB}, 95 \mathrm{~dB}\)4.
Name which keys are one half-step up and one half-step down from the following:1. \(\mathrm{D}\)2. \(E\)3. \(\mathrm{G} \#\)
Name which keys are one whole step up and one whole step down from the following:1. \(\mathrm{F}^{\#}\)2. \(E\)3. \(A^{b}\)
List the 12 notes forming an octave, beginning with the note \(C\).
Given that the frequency of \(\mathrm{C}_{4}\) is \(262 \mathrm{~Hz}\), find the approximate frequency of \(\mathrm{C}_{6}\).
Find the number of games in a single round-robin tournament for each of the following numbers of teams:1. 4 teams 2. 8 teams 3. 20 teams
Find the number of games in a single-elimination tournament for each of the following numbers of teams:1. 4 teams 2. 8 teams 3. 20 teams
If a person's height is \(6 \mathrm{ft} 2 \mathrm{in}\), what is the approximate length from their belly button to the floor rounded to the nearest inch if the ratio is golden?
If a circular row on a pinecone contains 21 scales and models the Fibonacci sequence, approximately how many scales would be found on the next circular row?
The 23 rd Fibonacci number is 28,657 and the 24 th is 46,368 . Show that the ratio of the 24 th and 23 rd Fibonacci numbers is approximately \(\phi\). Round your answer to the nearest thousandth.
Brushing your teeth with the water running continually uses about 4 gal of water. Turning the faucet off when you are not rinsing uses less than one-fourth of a gallon of water. Consider the recommendation to brush your teeth twice a day, how much water would be saved in a month ( 4 weeks) if the
Using the data in Your Turn 13.5, how much water would be saved in a month if one-third of a town's population of 15,000 turned the faucet off when brushing their teeth except when rinsing?
Using the data in Example 13.5, how much water would be saved in a year if one-sixth of the population of the state of Florida, which is approximately 21.6 million people, turned the faucet off when brushing their teeth except when rinsing for a year ( 52 weeks)?
A 40 in plasma television uses about \(175 \mathrm{~W}\). How many kilowatt-hours are needed to run the television in a month if the television is on for an average of 3 hours a day?
A dorm-sized Energy Star-rated refrigerator uses about \(375 \mathrm{~W}\) and runs for about 9 hours per day. What is the monthly cost of running the refrigerator if the electric rate is 14 cents per kilowatt-hour?
A toaster oven is labeled as \(2,000 \mathrm{~W}\). How much would it cost to warm leftovers from a meal for 15 minutes if the electric rate is 12 cents per kilowatt-hour?
A tiny home uses approximately \(12 \mathrm{~kW}\) of electricity per day. What size solar system would be needed to fuel \(80 \%\) of a home's needs for a month (30 days)?
How many milligrams of sodium chloride are there in \(200 \mathrm{~mL}\) of a \(0.9 \% \mathrm{w} / \mathrm{v}\) normal saline solution?
How many pills would be needed for a patient who has been prescribed \(25.5 \mathrm{mg}\) of a drug if each pill contains \(4.25 \mathrm{mg}\).
A patient is prescribed \(1.4 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered intramuscularly, divided into 2 doses per day. If the patient weighs \(60 \mathrm{~kg}\), how many milliliters of the drug should be given per dose?
A patient is prescribed \(2.5 \mathrm{mg} / \mathrm{kg}\) of a drug to be delivered intramuscularly, divided into 2 doses per day. If the drug is available in \(5 \mathrm{mg} / \mathrm{mL}\) and the patient weighs \(52 \mathrm{~kg}\), how many milligrams of the drug should be given per dose?
For the following exercises, use Figure 13.12.1. List all the names of those who have a path length of three from Uma.2. What is the length of the shortest path from Naomi to Vega?
Match each of the following sounds with a corresponding decibel level: live outdoor concert, birds chirping, window air conditioner, garbage disposal.1. \(40 \mathrm{~dB}\)2. \(60 \mathrm{~dB}\)3. \(80 \mathrm{~dB}\)4. \(100 \mathrm{~dB}\)
Name which keys are one half-step up and one half-step down from the following:1. \(F^{\#}\)2. \(\mathrm{B}\)3. \(G^{b}\)
Name which keys are one whole step up and one whole step down from the following:1. \(D^{b}\)2. \(C^{\#}\)3. \(\mathrm{E}\)
List the 12 notes forming an octave, beginning with the note \(\mathrm{G}\).
Given that the frequency of \(\mathrm{E}_{4}\) is \(330 \mathrm{~Hz}\), find the approximate frequency of \(\mathrm{E}_{2}\) rounded to the nearest whole number.
Find the number of games in a single round-robin tournament for each of the following numbers of teams:1. 5 teams 2. 12 teams 3. 25 teams
Find the number of games in a single-elimination tournament for each of the following numbers of teams:1. 5 teams 2. 12 teams 3. 25 teams
Determine the number of vertices in Graph \(S\).Use the given figure. a Graph S e d b Graph T Graph U e Graph V a e Graph W e
Identify the graph with the fewest edges.Use the given figure. a Graph S e d b Graph T Graph U e Graph V a e Graph W e

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Contemporary Mathematics 1st Edition OpenStax - Solutions

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